Math Problem Statement
Solution
The graph in the image shows a line with a negative slope crossing the y-axis and x-axis at specific points. To find the equation of the line, we can use the slope-intercept form of a linear equation, which is:
Where:
- is the slope of the line.
- is the y-intercept (the point where the line crosses the y-axis).
Step 1: Identify two points on the line.
From the graph, two clear points on the line are:
- , which is the y-intercept.
- , which is the x-intercept.
Step 2: Calculate the slope .
The formula for the slope between two points and is:
Substitute the points and :
Step 3: Write the equation.
Now that we have the slope and the y-intercept , the equation of the line is:
This is the equation of the line in slope-intercept form.
Let me know if you'd like further details or have any questions!
Related Questions:
- How do you find the slope from a graph if no clear points are given?
- What is the point-slope form of a line equation, and how does it relate to the slope-intercept form?
- How do you convert the equation from slope-intercept form to standard form?
- What does the slope tell us about the direction of the line?
- How can you verify if a point lies on a line given its equation?
Tip: Always check your points carefully when calculating the slope, especially for signs (positive or negative).
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Graphing
Slope-Intercept Form
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + b
Theorems
Slope-Intercept Form Theorem
Suitable Grade Level
Grades 8-10